international ground water modeling center

BOUNDARY CONDITIONS

By: Eileen P. Poeter and William L. Wingle

Boundary Types

Specified Head: a special case of constant head (ABC, EFG)

Constant Head: could replace (ABC, EFG)

Specified Flux: could be recharge across (CD)

No Flow (Streamline): a special case of specified flux (HI)

Head Dependent Flux: could replace (ABC, EFG)

Free Surface: water-table, phreatic surface (CD)

Seepage Face: h = z; pressure = atmospheric at the ground surface (DE)

• Specified Head: Head (H) is defined as a function of time and space.
• Constant Head: Head (H) is constant at a given location.

Implications: Supply Inexhaustible, or Drainage Unfillable

Example of Constant Head Boundary

Example of Specified Head Boundary

• Specified Flux: Discharge (Q) varies with space and time.
• No Flow: Discharge (Q) equals 0.0 across boundary.

Implications: H will be calculated as the value required to produce a gradient to yield that flux, given a specified hydraulic conductivity (K). The resulting head may be above the ground surface in an unconfined aquifer, or below the base of the aquifer where there is a pumping well; neither of these cases are desirable.

Boundary Flux Example #1 - Specified Flux

Boundary Flux Example #2 - No Flow

• Head Dependent Flux:

H₁ = Specified head in reservoir

H₂ = Head calculated in model

Implications:

• If H₂ is below AB, q is a constant and AB is the seepage face, but model may continue to calculate increased flow.
• If H₂ rises, H₁ doesn't change in the model, but it may in the field.
• If H₂ is less than H₁, and H₁ rises in the physical setting, then inflow is underestimated.
• If H₂ is greater than H₁, and H₁ rises in the physical setting, then inflow is overestimated.

• Free Surface: h = Z, or H = f(Z)

  
  e.g. the water table h = z

  

  or a salt water interface

  

  Note, the position of the boundary is not fixed!

Implications: Flow field geometry varies so transmissivity will vary with head (i.e., this is a nonlinear condition). If the water table is at the ground surface or higher, water should flow out of the model, as a spring or river, but the model design may not allow that to occur.

• Seepage Surface: The saturated zone intersects the ground surface at atmospheric pressure and water discharges as evaporation or as a downhill film of flow.

  The location of the surface is fixed, but its length varies (unknown a priori).

  

Implications: A seepage surface is not a head or flowline, and often can be neglected in large scale models.